Open Access
2013 Nontrivial Periodic Solutions of an n -Dimensional Differential System and Its Application
F. B. Gao
Abstr. Appl. Anal. 2013(SI44): 1-9 (2013). DOI: 10.1155/2013/140173


Two criteria are constructed to guarantee the existence of periodic solutions for a second-order n -dimensional differential system by using continuation theorem. It is noticed that the criteria established are found to be associated with the system’s damping coefficient, natural frequency, parametrical excitation, and the coefficient of the nonlinear term. Based on the criteria obtained, we investigate the periodic motions of the simply supported at the four-edge rectangular thin plate system subjected to the parametrical excitation. The effectiveness of the criteria is validated by corresponding numerical simulation. It is found that the existent range of periodic solutions for the thin plate system increases along with the increase of the ratio of the modulus of nonlinear term’s coefficient and parametric excitation term, which generalize and improve the corresponding achievements given in the known literature.


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F. B. Gao. "Nontrivial Periodic Solutions of an n -Dimensional Differential System and Its Application." Abstr. Appl. Anal. 2013 (SI44) 1 - 9, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 06306057
MathSciNet: MR3102659
Digital Object Identifier: 10.1155/2013/140173

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI44 • 2013
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